I am currently showing a viewController in my new storyboard below:
var storyboard : UIStoryboard = UIStoryboard(name: AccountStoryboard, bundle: nil)
var vc : W
You're definitely on the right track. Unfortunately when you reference a view controller by its storyboard ID it will ignore the fact it is embedded within anything. Same goes for segues when you segue to something embedded, the destination view controller will be the embedding controller, not the controller you're usually interested in. Anyhow, you should be able to fix the problem in a similar way you've done in Objective-C, so this is just an exercise in syntax porting.
Edit: Define storyboard name with string now
let storyboard : UIStoryboard = UIStoryboard(name: "AccountStoryboard", bundle: nil)
let vc : WelcomeViewController = storyboard.instantiateViewControllerWithIdentifier("WelcomeID") as WelcomeViewController
vc.teststring = "hello"
let navigationController = UINavigationController(rootViewController: vc)
self.presentViewController(navigationController, animated: true, completion: nil)
OR you can give your embedding view controller an ID and instantiate that instead.